Cluster expansion of the many-body Green operator

A scheme is presented for expressing the many-body Green operator of an int eracting system in terms of Green operators of systems with a fewer number of interacting particles. The method relies on an tract algebraic operator identity proved in this work. Furthermore, we present a hierarchical approx imation that reduces successively the many-body problem to a lower dimensio nal solvable problem. Recipes for higher order corrections are given and pr actical applications are pointed out. (C) 2000 Elsevier Science B.V. All ri ghts reserved.